%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN052+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 01:49:07 PM UTC 2026
% Result : Theorem 0.62s 1.02s
% Output : Refutation 0.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 37 ( 5 unt; 4 def)
% Number of atoms : 101 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 106 ( 42 ~; 39 |; 13 &)
% ( 9 <=>; 2 =>; 0 <=; 1 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 6 prp; 0-1 aty)
% Number of functors : 1 ( 1 usr; 1 con; 0-0 aty)
% Number of variables : 24 ( 0 sgn 21 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ! [X0] :
( p
<=> big_f(X0) )
=> ( p
<=> ! [X1] : big_f(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel22) ).
fof(f2,negated_conjecture,
~ ( ! [X0] :
( p
<=> big_f(X0) )
=> ( p
<=> ! [X1] : big_f(X1) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
( ( p
<~> ! [X1] : big_f(X1) )
& ! [X0] :
( p
<=> big_f(X0) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f4,plain,
( ( ? [X1] : ~ big_f(X1)
| ~ p )
& ( ! [X1] : big_f(X1)
| p )
& ! [X0] :
( ( p
| ~ big_f(X0) )
& ( big_f(X0)
| ~ p ) ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f5,plain,
( ( ? [X1] : ~ big_f(X1)
| ~ p )
& ( ! [X1] : big_f(X1)
| p )
& ! [X0] :
( ( p
| ~ big_f(X0) )
& ( big_f(X0)
| ~ p ) ) ),
inference(flattening,[],[f4]) ).
fof(f6,plain,
( ( ? [X0] : ~ big_f(X0)
| ~ p )
& ( ! [X1] : big_f(X1)
| p )
& ! [X2] :
( ( p
| ~ big_f(X2) )
& ( big_f(X2)
| ~ p ) ) ),
inference(rectify,[],[f5]) ).
fof(f7,plain,
( ( ~ big_f(sK0)
| ~ p )
& ( ! [X1] : big_f(X1)
| p )
& ! [X2] :
( ( p
| ~ big_f(X2) )
& ( big_f(X2)
| ~ p ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f6]) ).
fof(f8,plain,
! [X2] :
( big_f(X2)
| ~ p ),
inference(cnf_transformation,[],[f7]) ).
fof(f9,plain,
! [X2] :
( p
| ~ big_f(X2) ),
inference(cnf_transformation,[],[f7]) ).
fof(f10,plain,
! [X1] :
( big_f(X1)
| p ),
inference(cnf_transformation,[],[f7]) ).
fof(f11,plain,
( ~ big_f(sK0)
| ~ p ),
inference(cnf_transformation,[],[f7]) ).
fof(f13,definition,
( spl1_1
<=> p ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
fof(f17,definition,
( spl1_2
<=> ! [X2] : big_f(X2) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
fof(f18,plain,
( ! [X2] : big_f(X2)
| ~ spl1_2 ),
inference(avatar_component_clause,[],[f17]) ).
fof(f19,plain,
( ~ spl1_1
| spl1_2 ),
inference(avatar_split_clause,[],[f8,f17,f13]) ).
fof(f21,definition,
( spl1_3
<=> ! [X2] : ~ big_f(X2) ),
introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition]) ).
fof(f22,plain,
( ! [X2] : ~ big_f(X2)
| ~ spl1_3 ),
inference(avatar_component_clause,[],[f21]) ).
fof(f23,plain,
( spl1_3
| spl1_1 ),
inference(avatar_split_clause,[],[f9,f13,f21]) ).
fof(f24,plain,
( spl1_1
| spl1_2 ),
inference(avatar_split_clause,[],[f10,f17,f13]) ).
fof(f26,definition,
( spl1_4
<=> big_f(sK0) ),
introduced(definition,[new_symbols(definition,[spl1_4])],[avatar_definition]) ).
fof(f28,plain,
( ~ big_f(sK0)
| spl1_4 ),
inference(avatar_component_clause,[],[f26]) ).
fof(f29,plain,
( ~ spl1_1
| ~ spl1_4 ),
inference(avatar_split_clause,[],[f11,f26,f13]) ).
fof(f30,plain,
( $false
| ~ spl1_2
| ~ spl1_3 ),
inference(forward_subsumption_resolution,[],[f22,f18]) ).
fof(f31,plain,
( ~ spl1_2
| ~ spl1_3 ),
inference(avatar_contradiction_clause,[],[f30]) ).
fof(f32,plain,
( $false
| ~ spl1_2
| spl1_4 ),
inference(forward_subsumption_resolution,[],[f28,f18]) ).
fof(f33,plain,
( ~ spl1_2
| spl1_4 ),
inference(avatar_contradiction_clause,[],[f32]) ).
cnf(s1,plain,
( ~ spl1_1
| spl1_2 ),
inference(sat_conversion,[],[f19]) ).
cnf(s2,plain,
( spl1_1
| spl1_3 ),
inference(sat_conversion,[],[f23]) ).
cnf(s3,plain,
( spl1_1
| spl1_2 ),
inference(sat_conversion,[],[f24]) ).
cnf(s4,plain,
( ~ spl1_1
| ~ spl1_4 ),
inference(sat_conversion,[],[f29]) ).
cnf(s5,plain,
( ~ spl1_2
| ~ spl1_3 ),
inference(sat_conversion,[],[f31]) ).
cnf(s6,plain,
( ~ spl1_2
| spl1_4 ),
inference(sat_conversion,[],[f33]) ).
cnf(s7,plain,
spl1_1,
inference(rat,[],[s5,s2,s3]) ).
cnf(s8,plain,
~ spl1_4,
inference(rat,[],[s4,s7]) ).
cnf(s9,plain,
spl1_2,
inference(rat,[],[s1,s7]) ).
cnf(s10,plain,
$false,
inference(rat,[],[s6,s8,s9]) ).
fof(f34,plain,
$false,
inference(avatar_sat_refutation,[],[s10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN052+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n020.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Mon Sep 28 15:27:19 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.21 Running first-order theorem proving
% 0.07/0.21 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.62/1.02 % (244978)Detected formulas, will run a generic FOF schedule.
% 0.62/1.02 % (244986)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4121012659:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.62/1.02 % (244986)First to succeed.
% 0.62/1.02 % (244986)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-244978"
% 0.62/1.02 % (244987)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1815217597:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.62/1.02 % (244988)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2749626043:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.62/1.02 % (244985)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=3833203571:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.62/1.02 % (244983)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=2572807005:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.62/1.02 % (244984)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=1259479335:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.62/1.02 % (244989)dis-21_1_sil=8000:lcm=predicate:random_seed=2575477215:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 0.62/1.02 % (244987)Also succeeded, but the first one will report.
% 0.62/1.02 % (244988)Also succeeded, but the first one will report.
% 0.62/1.02 % (244989)Also succeeded, but the first one will report.
% 0.62/1.02 % (244986)Refutation found. Thanks to Tanya!
% 0.62/1.02 % SZS status Theorem for theBenchmark
% 0.62/1.02 % SZS output start Proof for theBenchmark
% See solution above
% 0.62/1.02 % (244986)------------------------------
% 0.62/1.02 % (244986)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.62/1.02 % (244986)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.62/1.02 % (244986)CaDiCaL version: 2.1.3
% 0.62/1.02 % (244986)Termination reason: Refutation
% 0.62/1.02 % (244986)Time elapsed: 0.001 s
% 0.62/1.02 % (244986)Peak memory usage: 89 MB
% 0.62/1.02 % (244986)Instructions burned: 1 (million)
% 0.62/1.02 % (244986)------------------------------
% 0.62/1.02 % (244986)------------------------------
% 0.62/1.02 % (244978)Success in time 0.275 s
% 0.62/1.02 % Vampire exiting
%------------------------------------------------------------------------------